The number 40800
40800 is a composite number with 72 divisors. Its prime factorisation is × 3 × × 17. Divisors (72): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30 … 40800.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 40800: a Harshad number: divisible by its digit sum 12.
- 2
40800 is composite. Its prime factorisation is
- 3
The divisors add up to 140616; without 40800 itself that is 99816, so 40800 is abundant (99816 is more than 40800). Euler's totient φ(40800) = 10240 numbers up to 40800 share no factor with it.
- 4
The digits of 40800 add up to 12, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 88 steps to reach 1.
LaTeX source of the formulas on this page
\[ 40800 = 2^{5} \times 3 \times 5^{2} \times 17 \]40800 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 72 |
| Sum of divisors | 140616 |
| Euler totient φ(n) | 10240 |
| Square | 1664640000 |
| Cube | 67917312000000 |
| Square root | 201.990099 (= 20√102) |
| Digit sum / digital root | 12 / 3 |
| Collatz steps to 1 | 88 |
| Scientific notation | 4.08 × |
40800 in other forms
| Form | Value |
|---|---|
| In words | forty thousand eight hundred |
| Binary (base 2) | 1001111101100000 |
| Octal (base 8) | 117540 |
| Hexadecimal (base 16) | 9F60 |
| Base 3 | 2001222010 |
| As time | 40800 seconds = 11 h 20 min 0 s |
Is 40800 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (40800 ÷ 2 = 20400) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (40800 ÷ 3 = 13600) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (40800 ÷ 4 = 10200) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | Yes (40800 ÷ 5 = 8160) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (40800 ÷ 6 = 6800) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (40800 ÷ 8 = 5100) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 3) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | Yes (40800 ÷ 10 = 4080) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (40800 ÷ 12 = 3400) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 40800 a prime number?
No. 40800 = × 3 × × 17, so it is divisible by 2.
What are the factors of 40800?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 32, 34, 40, 48, 50, 51, 60, 68, 75, 80, 85, 96, 100, 102, 120, 136, 150, 160, 170, 200, 204, 240, 255, 272, 300, 340, 400, 408, 425, 480, 510, 544, 600, 680, 800, 816, 850, 1020, 1200, 1275, 1360, 1632, 1700, 2040, 2400, 2550, 2720, 3400, 4080, 5100, 6800, 8160, 10200, 13600, 20400, 40800.
What is 40800 in binary?
1001111101100000 (hexadecimal 9F60, octal 117540).
What is the square root of 40800?
About 201.9901, exactly 20√102.
Is 40800 divisible by 3?
Yes. Its digits add up to 12, a multiple of 3.
What is special about the number 40800?
40800 is a Harshad number: divisible by its digit sum 12.